Trace formulas and continuous dependence of spectra for the periodic conservative Camassa–Holm flow

This article is concerned with the isospectral problem −f" +1/4f = z ωf + z²vf

for the periodic conservative Camassa–Holm flow, where ω is a periodic real distribution in H⁻¹ loc (R) and υ is a periodic non-negative Borel measure on . We develop basic Floquet theory for this problem, derive trace formulas for the associated spectra and establish continuous dependence of these spectra on the coefficients with respect to a weak⁎ topology.